#iterative function

[ghastmaskzombie]

do you ever just mess around with a complex graphing site and look for fractals? i do, apparently. i call this guy the gamma crab. i’m ninety-nine percent sure he’s a fractal, but he’s definitely my friend. math nerdery below the cut.

this is the limit approached by iterating the gamma function infinitely. the cyan sections converge on positive real numbers (though i don’t know which) while the black sections diverge. the origin is somewhere between the main bulb and the largest peanut. not pictured: two arms of scaffold-esque geometry extending infinitely up and down to the right, roughly following two curves that i see a lot in my experiments similar to this (infinite tetration, iterated factorial, iteration of z^c+c) but can’t find any meaning to.